Should I buy her a drink?

I'm meeting up with an old female friend that I haven't seen in years. We're meeting to grab some drinks and catch up. Even though I'm going into this meeting with the mentality of simply reconnecting with an old friend, she is definitely dating material. We're both single, she's really fun and cute. Should I buy her a drink? It's not a date and I don't want to make her uncomfortable by treating the meeting as a date. Would it be awkward to do this?